### Abstract

In the water resources field, there are emerging problems such as temporal changes of data and new additions of water sources. Non-mixture models are not efficient in analyzing these data because these models are developed under the assumption that data do not change and come from one source. Mixture models could successfully analyze these data because mixture models contain more than one modal. The expectation maximization (EM) algorithm has been widely used to estimate parameters of the mixture normal distribution for describing the statistical characteristics of hydro meteorological data. Unfortunately, the EM algorithm has some disadvantages, such as divergence, derivation of information matrices, local maximization, and poor accuracy. To overcome these disadvantages, this study proposes a new parameter estimation approach for the mixture normal distribution. The developed model estimates parameters of the mixture normal distribution by maximizing the log likelihood function using a meta-heuristic algorithm-genetic algorithm (GA). To verify the performance of the developed model, simulation experiments and practical applications are implemented. From the results of experiments and practical applications, the developed model presents some advantages, such as (1) the proposed model more accurately estimates the parameters even with small sample sizes compared to the EM algorithm; (2) not diverging in all application; and (3) showing smaller root mean squared error and larger log likelihood than those of the EM algorithm. We conclude that the proposed model is a good alternative in estimating the parameters of the mixture normal distribution for kutotic and bimodal hydrometeorological data.

Original language | English |
---|---|

Pages (from-to) | 347-358 |

Number of pages | 12 |

Journal | Stochastic Environmental Research and Risk Assessment |

Volume | 28 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Environmental Engineering
- Environmental Chemistry
- Safety, Risk, Reliability and Quality
- Water Science and Technology
- Environmental Science(all)

### Cite this

*Stochastic Environmental Research and Risk Assessment*,

*28*(2), 347-358. https://doi.org/10.1007/s00477-013-0753-7

}

*Stochastic Environmental Research and Risk Assessment*, vol. 28, no. 2, pp. 347-358. https://doi.org/10.1007/s00477-013-0753-7

**Meta-heuristic maximum likelihood parameter estimation of the mixture normal distribution for hydro-meteorological variables.** / Shin, Ju Young; Heo, Jun Haeng; Jeong, Changsam; Lee, Taesam.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Meta-heuristic maximum likelihood parameter estimation of the mixture normal distribution for hydro-meteorological variables

AU - Shin, Ju Young

AU - Heo, Jun Haeng

AU - Jeong, Changsam

AU - Lee, Taesam

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In the water resources field, there are emerging problems such as temporal changes of data and new additions of water sources. Non-mixture models are not efficient in analyzing these data because these models are developed under the assumption that data do not change and come from one source. Mixture models could successfully analyze these data because mixture models contain more than one modal. The expectation maximization (EM) algorithm has been widely used to estimate parameters of the mixture normal distribution for describing the statistical characteristics of hydro meteorological data. Unfortunately, the EM algorithm has some disadvantages, such as divergence, derivation of information matrices, local maximization, and poor accuracy. To overcome these disadvantages, this study proposes a new parameter estimation approach for the mixture normal distribution. The developed model estimates parameters of the mixture normal distribution by maximizing the log likelihood function using a meta-heuristic algorithm-genetic algorithm (GA). To verify the performance of the developed model, simulation experiments and practical applications are implemented. From the results of experiments and practical applications, the developed model presents some advantages, such as (1) the proposed model more accurately estimates the parameters even with small sample sizes compared to the EM algorithm; (2) not diverging in all application; and (3) showing smaller root mean squared error and larger log likelihood than those of the EM algorithm. We conclude that the proposed model is a good alternative in estimating the parameters of the mixture normal distribution for kutotic and bimodal hydrometeorological data.

AB - In the water resources field, there are emerging problems such as temporal changes of data and new additions of water sources. Non-mixture models are not efficient in analyzing these data because these models are developed under the assumption that data do not change and come from one source. Mixture models could successfully analyze these data because mixture models contain more than one modal. The expectation maximization (EM) algorithm has been widely used to estimate parameters of the mixture normal distribution for describing the statistical characteristics of hydro meteorological data. Unfortunately, the EM algorithm has some disadvantages, such as divergence, derivation of information matrices, local maximization, and poor accuracy. To overcome these disadvantages, this study proposes a new parameter estimation approach for the mixture normal distribution. The developed model estimates parameters of the mixture normal distribution by maximizing the log likelihood function using a meta-heuristic algorithm-genetic algorithm (GA). To verify the performance of the developed model, simulation experiments and practical applications are implemented. From the results of experiments and practical applications, the developed model presents some advantages, such as (1) the proposed model more accurately estimates the parameters even with small sample sizes compared to the EM algorithm; (2) not diverging in all application; and (3) showing smaller root mean squared error and larger log likelihood than those of the EM algorithm. We conclude that the proposed model is a good alternative in estimating the parameters of the mixture normal distribution for kutotic and bimodal hydrometeorological data.

UR - http://www.scopus.com/inward/record.url?scp=84891030986&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891030986&partnerID=8YFLogxK

U2 - 10.1007/s00477-013-0753-7

DO - 10.1007/s00477-013-0753-7

M3 - Article

AN - SCOPUS:84891030986

VL - 28

SP - 347

EP - 358

JO - Stochastic Environmental Research and Risk Assessment

JF - Stochastic Environmental Research and Risk Assessment

SN - 1436-3240

IS - 2

ER -